Neighborhood connected domination and colouring in graphs

A dominating set S of a connected graph G = (V;E) is a neighborhood connected dominating set (ncd-set) if the induced subgraph hN(S)i of G is connected. The neighborhood connected domination number nc(G) is the minimum cardinality of a ncd-set. The minimum number of colours required to colour all the vertices such that no two adjacent vertices have same colour is the chromatic number _(G) of G. In this paper we find an upper bound for sum of the ncd-number and chromatic number and characterize the corresponding extremal graphs.